Question

What am I doing wrong in this problem?
[5/(x-7)] + [2/(x+6)]

Answer 1

I turned them into \[\frac{ -30+14 }{ x+42 }\] with x cannot equal 7, -6, or -42

Answer 2

But my homework says it's wrong.

Answer 3

\[\frac{ -16 }{ x+42 }\]

Answer 4

Well, your LCD is not x+42... you need to multiply:

(x-7)(x+6)

to get the LCD. But you really don't need to "expand" that with FOIL (in fact, I wouldn't, because you may find that something will reduce at the end. So you need:

\[\frac{ 5(x+6)+2(x-7) }{ (x-7)(x+6) }\]

Answer 5

Simplify the numerator, and reduce anything if you are able to.

Answer 6

So I would have \[\frac{ 7x+16 }{ (x+6)(x-7) }\] with x cannot equal -6 and +7?

Answer 7

That's what I get. :)